The main difference seems to be verifiability down to the firmware level.
Nitro enclaves does not provide measurements of the firmware[0], or hypervisor, furthermore they state that the hypervisor code can be updated transparently at any time[1].
Apple is going to provide images of the secure enclave processor operating system(sepOS), as well as the bootloader.
It also sounds like they will provide the source code for these components too, although the blog post isn't clear on that.
[0]: https://docs.aws.amazon.com/enclaves/latest/user/set-up-atte....
[1]: https://docs.aws.amazon.com/pdfs/whitepapers/latest/security...